{"id":29584,"date":"2025-06-21T07:32:29","date_gmt":"2025-06-21T07:32:29","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=29584"},"modified":"2025-06-21T07:32:31","modified_gmt":"2025-06-21T07:32:31","slug":"after-decaying-for-48-hours-1-16-of-the-original-mass-of-a-radioisotope-sample-remains-unchanged","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/after-decaying-for-48-hours-1-16-of-the-original-mass-of-a-radioisotope-sample-remains-unchanged\/","title":{"rendered":"After decaying for 48 hours, 1\/16 of the original mass of a radioisotope sample remains unchanged"},"content":{"rendered":"\n<p>After decaying for 48 hours, 1\/16 of the original mass of a radioisotope sample remains unchanged. What is the half life of this radioisotope<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n<p><strong>Correct Answer: 12 hours<\/strong><\/p>\n\n\n\n<p>To determine the half-life of the radioisotope, we must understand how radioactive decay works. A half-life is the time it takes for half of a radioactive substance to decay. Every time a half-life passes, only half of the remaining substance is left.<\/p>\n\n\n\n<p>In this problem, we are told that after 48 hours, only <strong>1\/16<\/strong> of the original mass remains. This implies that the substance has gone through multiple half-lives because the mass keeps halving with each one. Let\u2019s figure out how many half-lives are required to reach <strong>1\/16<\/strong> of the original amount.<\/p>\n\n\n\n<p>We start with 1 (the whole original mass):<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>After 1 half-life: 1\/2 remains<\/li>\n\n\n\n<li>After 2 half-lives: 1\/4 remains<\/li>\n\n\n\n<li>After 3 half-lives: 1\/8 remains<\/li>\n\n\n\n<li>After 4 half-lives: 1\/16 remains<\/li>\n<\/ul>\n\n\n\n<p>So, it takes <strong>4 half-lives<\/strong> to decay to 1\/16 of the original amount. We are told this process took <strong>48 hours<\/strong>.<\/p>\n\n\n\n<p>To find the half-life, divide the total time by the number of half-lives:<\/p>\n\n\n\n<p><strong>48 hours \u00f7 4 = 12 hours<\/strong><\/p>\n\n\n\n<p>Therefore, the half-life of the radioisotope is <strong>12 hours<\/strong>.<\/p>\n\n\n\n<p>This method of calculation relies on exponential decay, which is common for radioactive substances. Each half-life reduces the amount of material to half of what it was in the previous period. This consistent halving leads to a geometric sequence, where the remaining fraction after <em>n<\/em> half-lives is (1\/2)^n. By recognizing the pattern and matching it to the elapsed time, we can accurately calculate the half-life of any radioactive sample using this approach.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>After decaying for 48 hours, 1\/16 of the original mass of a radioisotope sample remains unchanged. What is the half life of this radioisotope The correct answer and explanation is: Correct Answer: 12 hours To determine the half-life of the radioisotope, we must understand how radioactive decay works. A half-life is the time it takes [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-29584","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/29584","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=29584"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/29584\/revisions"}],"predecessor-version":[{"id":29585,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/29584\/revisions\/29585"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=29584"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=29584"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=29584"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}